Question: Simplify the following expression: $\dfrac{6q}{12q^2}$ You can assume $q \neq 0$.
Answer: $ \dfrac{6q}{12q^2} = \dfrac{6}{12} \cdot \dfrac{q}{q^2} $ To simplify $\frac{6}{12}$ , find the greatest common factor (GCD) of $6$ and $12$ $6 = 2 \cdot 3$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(6, 12) = 2 \cdot 3 = 6 $ $ \dfrac{6}{12} \cdot \dfrac{q}{q^2} = \dfrac{6 \cdot 1}{6 \cdot 2} \cdot \dfrac{q}{q^2} $ $\phantom{ \dfrac{6}{12} \cdot \dfrac{1}{2}} = \dfrac{1}{2} \cdot \dfrac{q}{q^2} $ $ \dfrac{q}{q^2} = \dfrac{q}{q \cdot q} = \dfrac{1}{q} $ $ \dfrac{1}{2} \cdot \dfrac{1}{q} = \dfrac{1}{2q} $